Exponential Runge-Kutta Methods for the Multispecies Boltzmann Equation (Communications in Computational Physics, 2020)
This paper generalizes the exponential Runge-Kutta asymptotic preserving(AP) method developed in [G. Dimarco and L. Pareschi, SIAM Numer. Anal., 49 (2011),pp. 2057–2077] to compute the multi-species Boltzmann equation. Compared to thesingle species Boltzmann equation that the method was originally applied to, thisset of equation presents a new difficulty that comes from the lack of local conservationlaws due to the interaction between different species. Hence extra stiff nonlinearsource terms need to be treated properly to maintain the accuracy and the AP property.The method we propose does not contain any nonlinear nonlocal implicit solver,and can capture the hydrodynamic limit with time step and mesh size independent ofthe Knudsen number. We prove the positivity and strong AP properties of the scheme,which are verified by two numerical examples.